Average Error: 7.3 → 1.3
Time: 4.8s
Precision: 64
\[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
↓
\[\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}\]
\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}
↓
\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}
double f(double x, double y, double z, double t) {
        double r825707 = x;
        double r825708 = y;
        double r825709 = z;
        double r825710 = r825708 - r825709;
        double r825711 = t;
        double r825712 = r825711 - r825709;
        double r825713 = r825710 * r825712;
        double r825714 = r825707 / r825713;
        return r825714;
}
↓
double f(double x, double y, double z, double t) {
        double r825715 = x;
        double r825716 = cbrt(r825715);
        double r825717 = r825716 * r825716;
        double r825718 = y;
        double r825719 = z;
        double r825720 = r825718 - r825719;
        double r825721 = cbrt(r825720);
        double r825722 = r825721 * r825721;
        double r825723 = r825717 / r825722;
        double r825724 = t;
        double r825725 = r825724 - r825719;
        double r825726 = cbrt(r825725);
        double r825727 = r825726 * r825726;
        double r825728 = r825723 / r825727;
        double r825729 = r825716 / r825721;
        double r825730 = r825729 / r825726;
        double r825731 = r825728 * r825730;
        return r825731;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.3
Target8.1
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;\frac{x}{\left(y - z\right) \cdot \left(t - z\right)} \lt 0.0:\\ \;\;\;\;\frac{\frac{x}{y - z}}{t - z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\left(y - z\right) \cdot \left(t - z\right)}\\ \end{array}\]

Derivation

  1. Initial program 7.3

    \[\frac{x}{\left(y - z\right) \cdot \left(t - z\right)}\]
  2. Using strategy rm

  3. Applied associate-/r*2.1

    \[\leadsto \color{blue}{\frac{\frac{x}{y - z}}{t - z}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt2.7

    \[\leadsto \frac{\frac{x}{y - z}}{\color{blue}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}}\]

  6. Applied add-cube-cbrt3.0

    \[\leadsto \frac{\frac{x}{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  7. Applied add-cube-cbrt3.1

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  8. Applied times-frac3.1

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}}{\left(\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}\right) \cdot \sqrt[3]{t - z}}\]

  9. Applied times-frac1.3

    \[\leadsto \color{blue}{\frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}}\]

  10. Final simplification1.3

    \[\leadsto \frac{\frac{\sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}}{\sqrt[3]{t - z} \cdot \sqrt[3]{t - z}} \cdot \frac{\frac{\sqrt[3]{x}}{\sqrt[3]{y - z}}}{\sqrt[3]{t - z}}\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Random.Distribution.Triangular:triangularCDF from random-fu-0.2.6.2, B"
  :precision binary64

  :herbie-target
  (if (< (/ x (* (- y z) (- t z))) 0.0) (/ (/ x (- y z)) (- t z)) (* x (/ 1 (* (- y z) (- t z)))))

  (/ x (* (- y z) (- t z))))